Question

letters a, b, c, and d are angles measures. which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? choose three correct answers. a = c b + d = 180° b + c = 180° a = d c = d

Explanation:

Step1: Recall the properties of parallel lines cut by a transversal

When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and consecutive - interior angles are supplementary.

Step2: Analyze each equation

• For \(a = c\): If \(a\) and \(c\) are corresponding angles, then \(m\parallel n\) by the corresponding - angles postulate.
• For \(b + d=180^{\circ}\): If \(b\) and \(d\) are consecutive - interior angles, then \(m\parallel n\) by the consecutive - interior angles converse.
• For \(a = d\): If \(a\) and \(d\) are alternate - exterior angles, then \(m\parallel n\) by the alternate - exterior angles converse.

Step3: Analyze the non - valid equation

• For \(b + c = 180^{\circ}\): \(b\) and \(c\) are adjacent angles. Their sum being \(180^{\circ}\) does not give information about the parallelism of \(m\) and \(n\).
• For \(c = d\): \(c\) and \(d\) are not in a relationship (such as corresponding, alternate - interior, alternate - exterior, or consecutive - interior) that can be used to prove parallelism.

Answer:

\(a = c\), \(b + d = 180^{\circ}\), \(a = d\)